FIGURE 4.-Relation between annual minimum 7-day and annual minimum 30-day discharges, 1926-71.
facilities, and funds. Manpower and funding limi- possibilities of developing a new model. There tations, in conjunction with a relatively short fore, two existing reservoir-system m0dels (Jen project duration (2.5 years), severely limited the nings and others, 1976) were considered for po-
H6 tential application to the Willamette River basin already assembled a considerable amount of di reservoir system. These models are the HEC-3 rectly applicable input data. This advantage, model developed by the U.S. Army Corps of En combined with the fact that no revisions of the gineers ( 1968) and the SIMYLD II model de HEC-3 program were required, resulted in the veloped by the Texas Water Development Board selection of HEC-3 as the most directly applicable ( 1972). reservoir-system model for this study. The HEC-3 model exhibited major advantages INPUT DATA PREPARATIOP as follows: ( 1) 8 of the 13 reservoirs in the Wil lamette River basin reservoir system are used for The computation time interval selected for the power generation, and power-release modeling is modeling effort was 1 month. Generally, a possible with HEC-3 but is not possible with monthly basis would be inadequate for estimat SIMYLD II; (2) most of the minimum-flow re ing low flows of short duration. However, the Wil quirements in the Willamette River basin are lamette River at Salem exhibits a very Etrong re variable by season which can be expressed using lationship between 7 -day and 30-day annual HEC-3, but these requirements must be ex minimum low-flow rates. Figure 4 shows this re pressed as a yearly average in SIMYLD II; and (3) lationship as computed from 1926--71 st~eamflow the more flexible expression of operating rules data. Figure 5 shows a similar relationship permitted by HEC-3 made it possible to define between 7 -day and monthly annual ninimum better the actual operating rules of the Wil low-flow rates. The standard errors of these two lamette River basin reservoir system. These limi relationships are about 3 percent and 18 percent, tations of SIMYLD II could have been overcome respectively. The higher error of the latter is due by additional programing had sufficient time to the fact that the minimum 30-day and been available. minimum monthly flow rates can be sigrificantly The Portland District of the Corps of Engineers different when the 30-day low-flow per~od over had used the HEC-3 model for preliminary laps calendar-month boundaries. However, this analyses in the Willamette River basin and had problem is considerably outweighed by the ad-
ANNUAL MINIMUM MONTHLY DISCHARGE, IN CUBIC METRES PER SECOND
8 100 150 200 250 ~~ 200 t3o ~ p:;U 00 -<~ ::r:;rn A P::z UP:: -1=0~- ~p:; :::>E-1 _u~:::> A ~~ z~ A -~ ~0 4 A ~~ A AA A ~1=0 ...:loo. A -< 0 100 ...:l:::> :::>z ..:r:U z~ A :::>z Z:::> 1. A z-z ..:r:g -< E-1 ~ 2 2 4 6 8 10
ANNUAL MINIMUM MONTHLY DISCHARGE, IN THOUSANDS OF CUBIC FEET PER SECOND
FIGURE 5.-Relation between annual minimum 7-day and annual minimum monthly discharges, 1926-71.
H7 vantages of using monthly data in the model (that unaffected by regulation and (or) diversions. A is, availability of data and computation reduc satisfactory relationship could not always be ob 1 tion). Also, since the total travel time for flows to . tained using a single index station, ir which cases traverse the length of the basin is only on the two index stations were used. Selection of the order of days, the monthly time frame eliminates applicable index station(s) for each control point the need of any streamflow routing. involved a trial-and-error process to simultane ously minimize the standard error and maximize STREAMFLOW DATA the correlation coefficient of the relationship. At a The HEC-3 model requires definition of the few control points the relationships developed by total streamflow that would occur at each control using gaging station data were judged inadequate point under natural conditions (that is, unaf because the standard error was too high and (or) fected by regulation, flow diversions, and so the correlation coefficient was too lovr. To develop forth). The U.S. Army Corps of Engineers (writ acceptable relationships at these control points it ten commun., 1974> provided adequate input data was necessary to use one (or two) upstream con for unregulated, monthly streamflow at all con trol points as the index station( s ). Table 3 sum trol points for the period 1926-69. They had de marizes the final relationships used for extending veloped these data using correlation and water the unregulated streamflow for each control budget computations. It was deen1ed imperative point. to extend these natural streamflow data through RESERVOIR CHARACTERISTICS the severe drought year of 1973 (which was also Physical properties of the reservoirs plus power the first year of intensive data collection for DO generation data and operating rules were ob modeling). tained from the Portland District of the U.S. Therefore, at each control point, an attempt Army Corps of Engineers (written commun., was made to develop a relationship for extending 1974). Figure 6 illustrates a typical operating the Corps data by correlating the Corps data with rule curve that is applicable to each reservoir. observed streamflow at an index station. An The storage data used to define the individual index station, in this context, is defined as a rule curves for the HEC-3 model are tabulated in streamflow gaging station at which streamflow is table 4.
TABLE 3.-Relationships used to extend unregulated, monthly streamflouJ through 1973
Control Fn·st Second Period of pomt mdex mdex SE 3 record number' statwn" statwn2 I percent I R" used
4 10 ------1448 141 0.561 113~ 1 1 10.6 0.990~ 1959--69 11 H7.5 1~65 .5.190 0 630 0.360 10.0 .9919 1940--69 2~ 15 1
1:2 ------15~5 152.5 :2.365 .690 .:213 16 6 .9910 19~0--69 ~1 1475 141 7.506 .9~.5 1"1 10.6 .9916 1940--69 1:3 1525 141 .980 1.058 1"1 12.6 .9953 19~0--69 u 15~5 ,., 1 ')')'1 1.005 ,., 9-! .9978 19~0--69 ~2 1.525 15~5 2.665 .62~ .478 10.4 9973 19~0--69 ~3 1.5:25 1475 16.223 .3~9 .605 9.6 .99~7 19~0--69 1.5 1592 1'1 3.58 1.200 14 1 13.0 .984.5 19.58-69 16 1611 1615 1 797 .868 .146 1~.2 9937 1964--69 4 ~~ 6 9~3 141 17 773 .674 1 1 HA 9738 19~0--69 4 ~.5 "9~~ 141 203 1.266 1 1 12.2 9889 1940--69 18 16615 1670 1.291 .929 .176 9.8 .9982 19~1-69 ~6 ------166.5 1670 1.011 1.264 -066 88 .9983 1941-69
~8 ------"9~.5 "9~6 2.419 .838 134 13.8 .9877 19~1-69 21 1850 1870 3.061 .7.5.5 .230 1~ 6 .9922 19~8-69 32 18.50 1870 ~.17.'1 .820 17.5 86 .9973 19~8--69 39 18.50 1870 .5.181 730 .27.5 85 9974 1948-69 (41 :2:3 ------1790 1'1 6 719 919 76 .9906 1940--69 25 15 1
~0 ------1825 1790 10 11.5 .210 .703 12.5 .9867 1940--69 ~9 18.50 14 1 :29 36S .840 ,., 1.5.4 .988~ 19~0--69 .50 6 948 "949 l.178 .88.5 .160 12.7 .9906 1941-69 .51 "950 ,., 707 1.0.58 1"1 1.5.0 .98.59 19~1-69
Month!) flow at a control pomt can be computed hy X =a }_·bzc. where X= monthly flow at the control pomt; Y =monthly flow at the first index station; and Z =monthlv flow at the second mdex statwn
1See figure 1 for locatiOns and table 1 for reserYmr names °Four-digtt statwn numbers are the yyyy porhon of the USGS gaging-statwn number 14--yyyyOO. "SE, the standard error of estimate, and R. the correlatwn coefficient, are measures of the goodness of fit of the computed data to the observed data I Draper and Smith, 19661. "Best correlation obtained by usmg only one index station Monthly flows at these control points are computed by X =a yb. 'These control pomt5 are at small reregulating reservoirs JUSt downstream from large resen·oirs and reqmre no streamflow data since there iS no additwnal mflow between the two reservoirs. "Correlation with gagmg-statwn data considered unacceptable. Correlation was made usmg one lor two 1upstream control point Is 1as mdex statwnls 1. 9xx denotes flows computed at control pomt xx usmg the relatwnship between control point xx and its mdex statwnl s 1
HS --- ~---
JAN FEB MAR APR MAY JUNE JULY AUG SEP OCT NOV IEC
@ Major Flood Period--reservoir held to minimum elevation (storage) for flood control. @ Conservation Storing Period--reservoir filled for conservation purposes. Conservation Release Period--stored water released as needed. Minimum Reservoir Elevation (Storage)--minimum "storage level" specified for HEC-3. ® Top of Power Storage--next to lowest "storage level'' specified for HEC-3. ® Bottom of flood control pool for "dry conditions" (whereas H re presents "ideal", "normal", or "average" conditions.) @ Intermediate "storage levels" may be used to control the rate of depletion below "ideal" for various degrees of "below average" conditions, and among reservoirs in the system. @ Bottom of Flood Control Pool--next to highest "storage level" specified for HEC-3. ([) Maximum Reservoir Elevation (Storage)--maximum "storage level" specified for HEC-3.
FIGURE 6.-Typical rule curve of reservoir operation in the Willarnette River basin.
H9 TABLE 4.-Rule curve storage data used in HEC-3
Control Storage Reservmr storage 1 thousands of acre-feet 1 pomt level number' number" Jan Feb. Mar. Apr. May .June .July Aug Sept. Oct. Nov. Dec.
I .356 6 .s 340 325 295 238 156 250 290 330 156 10 4 } 350.6 350.6} 325 290 260 230 } 156 3 156 107
7 456 6 430 410 345 5 'l 118 8 245 118.8 118.8 11 4 J 265 340 420 443.1 443.1} 410 360 310 } 3 2 118.8 1 106.6
24 1-7 All months: 25.4
7 125 6 117.5 110 90 6.5 30 100 95 65 35 15 12 } 10 58 84 109 117.5 l1o 10 } 50 45 22.5 17.5 13 5 J 10
7 32.9 6 31.75 30 25 18 5 26 10 ~ 2.9 31.75 18 l39 2.9 2.9 13 4 10.8 19 27 31 75 31.75 16 8.4 5.9 f . 3 J 11.9 10 7.7 5.9 \. I 2.9
7 77.5 6 -~ 71.9 70 55 40 5 65 .57 40 25 24 42 5 60.5 71.9 )~ 14 4 35 35 25 14 3 J 30 24 19 14 s
7 219 .. 27 6 207.97 200 190 165 115 .5 6404 127 162 195 207.97 l6404 6404 15 4 } 200 190 160 130 105 J . 3 64.04 54 15
7 89.1 6 82.8 77.5 67.5 52 5 t .37.5 .57 76.5 82.8 I 5.8 4 16 4 } 80 70 50 30 3 J ' 4 7 116.9 6 5 ~ 18 4 -!3 81 101 2 101.2 1012 97.5 92.5 85 32.5 3 .-, } ' 7 430 6 410 400 370 338 265 5 't 160 280 336 392 HO 160 21 -! ) -!00 350 300 255 205 }160 3 J 160 97
7 61 6 38 5 l 31 38 46 53 .. 5 56 56 56 56 56 31 22 4 } 36 } 31 3 31 ' 27 4 7 455 6 434 -!13 386 350 262 5 1.55 284 355 422 43-! 155 23 4 } } 425 395 345 295 245 } 1.55 3 155 115 HlO TABLE 4.-Rule curue storage data used in HEC--3-Continued
Control Storage Resenmr storage 1thousands ol acre-teet> pomt len•I number2 number' .Jan Feb . Mar Apr Ma\' .June ,July Aug. Sept Oct NO\ Dec
25 1-7 All months· 4.53
1 See figure 1 for locations and table 1 for reservOir names. 2 See figure 6 for storage-level definitwns. Storage level numbers m this table coinnde with lettered items m figure 6 as follows: Levels 1 through 3 corrEspond to hnes D. E. and F: levels 4 and 5 are within region G: and levels 6 and 7 correspond to hnes H and I.
DIVERSION DATA this nature, thereby eliminating the need for The Corps also provided the diversion data calibration. (written commun., 1974) which they had obtained MODEL VERIFICATION from the Bureau of Reclamation. These data re An important aspect of any modeling effort is flect net depletions attributable to irrigation and model verification. That is, model results must be municipal and industrial water-supply demands. compared to observed, "real world" data to judge Table 5 summarizes the estimated net depletions whether or not the model is a valid predictive (withdrawals from the system) or return flows tool. (returns of excess withdrawals to the system) for The present reservoir system of 13 reservoirs in the years 1970, 1980, 2000, and 2020 at each di the Willamette River basin was not ccmpleted version point (fig. 1). until 1968. To avoid any anomalies that may CLIMATOLOGICAL DATA have existed in the operation of the system with the addition of the last few reservoirs, tr. e period Evaporation data used in the HEC-3 model are of 1970 through 1973 was selected for the verifi computed from the relationships shown in figure cation procedure. The 1973 reservoir-sys-l;em con 7. These relationships were obtained from the figuration and operating rules were defined in the U.S. Army Corps of Engineers (written commun., model and 1970 (table 4) diversions were assumed 1974). These data, reflecting total evaporation, representative of water demands for the verifica could be adjusted to reflect net evaporation by tion period. Unregulated monthly streamflow and adding average basin precipitation to each value. evaporation data for 1970-73 were used to define However, this represented a significant data the system inputs and losses. preparation effort and was ignored for the pur Table 6 (lines 6 and 7) summarizes the stream poses of this report. flow computed by HEC-3 (Qcl and the observed
OTHER DATA streamflow (Q 0 ) for the Willamette Piver at Salem for the period 1970-73. Both monthly and The Corps (written commun., 1974) also pro average annual data are shown. Also tabulated vided the following miscellaneous data: ( 1) Oine 8) is the total error of each of the computed minimum desired flows at all control points, (2) values (total Qc error in percent of Q 0 ). Differ maximum desired flows at all control points, and ences between model results and observed aver ( 3) all of the data pertaining to shortage declara age annual streamflow at Salem are considered tion (permissible depletion of desired reservoir very acceptable. Comparisons of nonthly storage to provide desired flows) in the reservoir streamflow values range more widely, from poor system. to very good. These total Q c errors are due to differences be MODEL CALIBRATION tween the model and the real world for ( 1) inflows Many types of models (such as DO models and to and losses from the system and (2) definition streamflow-routing models) must be calibrated. and operation of the reservoir system. A mass As discussed by Hines, Rickert, McKenzie, and volume balance of an entire reservoir syst.em may Bennett (1975), this procedure is required to ad be expressed as just certain model parameters so that model re (1) sults (for a particular set of observed input data) IL-Q=~, adequately represent the observed Hreal world" where IL represents an algebraic summation of results. HEC-3 contains no model parameters of all inputs to the system and all losses from the
H11 TABLE 5.-Flow diversion data used in the HEC-3 model
Net monthly depletwn !return fl.ow1 2 in cub1c feet per second Control pomt number' Year Jan Feb. Mar. Apr. May June July Aug Sept. Oct. Nov. Dec.
1970 1 6 19 20 16 5 0 1 41 1980 1 8 24 26 21 6 I 1 I 1 2000 4 4 14 38 40 34 11 0 4 2020 5 6 18 52 54 46 17 2 5
1970 3 3 3 3 15 44 47 37 9 121 I 11 3 1980 It' I 42 2 4 3 4 24 74 78 64 15 141 2 2000 3 3 3 47 148 158 130 .34 1151 181 1 2020 11 10 10 56 177 187 15.3 .38 1141 1101 5
1970 34 33 33 37 67 160 197 161 86 42 38 35 1980 .53 50 51 .56 107 245 306 254 1.38 6f 59 56 2000 8:3 84 79 86 215 551 657 529 278 104 94 87 2020 124 124 117 128 305 764 931 740 393 158 137 131
1970 ------1161 I 131 1141 1151 1111 151 1211 1211 1221 1201 1141 1161 1381 1301 1311 45 1980 ------1291 1271 1261 1281 1161 3 1211 1271 1371 2000 ------1461 1431 1401 1461 1111 52 18 121 1451 1701 1521 1501 2020 ------1801 1711 1671 1751 1 151 108 62 1581 11151 1921 1871
1970 9 11 10 11 33 91 98 80 33 11 13 9 46 1980 8 10 9 10 54 58 174 1:39 50 8 10 8 2000 14 17 16 17 120 365 393 302 122 7 14 14 2020 19 24 22 23 117 349 377 285 112 9 13 18
1970 17 24 21 22 57 146 148 99 46 16 27 16 1980 48 9 17 16 17 84 227 234 140 43 1151 10 1 2000 191 9 9 9 125 400 38.3 224 22 1701 1351 151 2020 7 33 31 3.3 126 -!42 410 211 16 1931 1341 161
1970 17 19 18 19 41 10.5 112 83 47 21 24 14 1980 39 16 17 17 17 49 126 139 102 53 17 2.3 15 2000 1191 1111 191 1101 231 754 811 551 179 15.31 1341 1181 2020 181 2 •) ') 232 768 829 543 190 1541 1211 1171
1970 6.3 66 62 65 157 .374 422 320 174 60 66 63 1980 40 87 92 1)5 90 2.36 548 631 475 250 78 91 86 2000 109 11.3 104 109 .342 890 994 758 .389 105 110 111 2020 140 142 131 138 405 1,044 1.185 898 478 1.35 141 137
1970 1 3 5 11 9 :3 0 0 •) 49 1980 4 6 14 .3.3 .31 16 4 1.31 .3 2000 0 .3 17 51 4.3 22 1.31 1111 141 0 2020 0 4 .35 12.3 120 68 14 I 191 171 141
1970 1171 1141 I 151 1161 39 161 175 107 22 1301 121 I 1221 .50 1980 1341 1.3.3r 1291 1311 90 .338 384 230 47 1671 1511 1491 2000 1.341 1281 r251 r271 150 568 591 377 84 1851 1721 1381 2020 1181 191 181 191 194 722 756 469 129 1951 1651 1.351
1970 24 45 41 44 .300 883 966 631 239 1411 28 14 1980 51 1111 21 28 27 46.3 1,370 1,538 964 .304 11601 1521 1471 2000 1181 53 4B 48 877 2,797 2,971 2,134 668 12391 1831 1161 2020 29 113 110 105 864 2,892 2,968 1.955 610 12951 1881 10
'See figure 1 for locatwns. 2 Values m parentheses md1cate return flows system, Q is the system output, and llS is the net Table 6 (lines 1-3) summarizes the values of summation of the storage change in all reservoirs IL0 , ILc, and the ILc error. The latter term is com In the system. The IL term is not directly ob puted as served (nor directly computed by the model) but can be estimated from observed (or computed) ILc error= xlOO. (3) values ofQ and llS. Therefore, rewriting equation 1 and subscripting with o for terms related to ob served data and c for terms related to computed Also tabulated are the ilS0 and llSc values (lines 4 values (model results) yields and 5). The small reregulating reservoirs (Big Cliff and Dexter) are not included in llS because (2a) ( 1) observed data are not available and (2) there and was a constant zero storage change for these res ervoirs in the HEC-3 model. Over 90 percent of (2b) the ILc values, which are based on the model re-
H12 AVERAGE MONTHLY AIR TEMPERATURE AT EUGENE, IN DEGREES CELSIUS
5 10 15 20 9
1. Evaporation rate, Er, in inches per month per acre of surface area is 8 Er = 0. 7 Ep· 2. Total reservoir evaporation, 200 E, in acre-feet is E = A(Er)/12 where A is reservoir surface area. 00. 3. Evaporation is considered 7 ~ 00. negligible for the months t~ ~ ::t: November through March. .,....~ u ,.-.; ~ 25 H 25 ~ 6 z 150 0 ~ ~ z "< g ~ 0 E-~ 0.. ~ "< ~=~ > 5 0 ~ ~" ~ z > < ~ 0.. z ~ ~: < ~'t:l > 0: ~ 1'1:;:1 0: ~t:l 2 50
40 45 50 55 60 65 70
AVERAGE MONTHLY AIR TEMPERATURE AT EUGENE, IN DEGREES FAHRENHEIT
FIGURE 7.-Evaporation relations for the Willamette River basin.
H13 TABLE 6.-Summary of model verification results
Average Year Lme Type of data .Jan Feb Mar. Apr. May June .July Aug. Sept. Oct. Nov. Dec. annual
IL0 !cubic feet per second I _____ 91,190 39,560 25,830 18,740 21,900 8,251 3,719 2,505 3.744 6,524 29,460 43,010 24,520 ILc lcuhic feet per second!_ 81,570 .38,210 27.860 21,540 24,440 8,676 3.592 2,124 3,601 7,1K6 31,260 311,440 24,010 3 ILc error !percent of!L,)i ______-10.6 -3.4 79 15.0 11.6 5.1 -.34 -15.2 -3.8 10.2 6.1 -10.6 -2.1 4 .:lS" nmverted to monthly flow_ 18,770 -17,490 7,419 5,025 2,771 -564 -3,350 -.5,025 -5,295 -6,206 -1,208 -3,599 -594 11,720 -1,355 -8,882 0 -75 1970 5 .:lSc rate !cubic feet per second! G,.304 Hl72 ::l,245 -451 -3,412 -4,856 -3,356 -5,274 6 Q 0 !cubic feet per second! ______72,420 .57,050 Hl,410 1.3,710 19,130 S,t\15 7,069 7,5.30 9,039 12,730 30,710 46,610 25,110 7 Qc !cubic feet per second! 69,850 39,56(1 21,560 16,670 21,200 9,127 7,004 6,834 6,9.57 12,460 40,140 38,440 24,090 8 Q rota!.----~------3.5 -30 7 17.1 21.6 10.8 3.5 -.9 -9.2 -23.0 -2.1 30.7 -17.5 -4.1 9 efror due tulLe t>rrur !percent ofQ0 1 _ -13 3 -2.4 11.1 20.5 13.3 4.8 -1.8 -.5.1 -1.6 5.2 5.8 -9.8 -2.0 10 due to reservou·-storage error __ 9.7 -21'1.3 6.1 1.1 -2.5 -1.3 9 -4 2 -21 5 -7.3 24.9 -7 7 -21
IL 0 I cubic feet per second! ______86,830 39,ROO -~1.8011 38,140 21'1,610 19,430 S,831 4,126 6,768 7,757 3.5,500 63,830 32,640 ILc tcubic feet per second I_ 79,720 :36,770 51,8:30 40,010 28,8.50 19,170 8,170 3,909 6.70.5 8,580 39,900 .'i6,340 31,680 3 ILc error Ipercent of IL 0 1 ______-8 2 -7.6 .1 4.9 8 -13 -7.5 -5.2 -.9 10.6 12.4 -11.7 -2.9 4 .:lS0 converted to monthly flow_ 9,735 263 6,145 4,822 4,545 -21 -612 -5,595 -5,922 -8,453 1,815 -8.296 -138 5 .:lSc rate !cubic feet per second I __ 9,043 2,622 -1,410 -3,.5.52 -3,267 -9,160 -8,882 0 0 1971 6,428 6,289 1,912 43 6 Q 0 !cubic feet per second! 77,100 39,G40 4.5.61)0 33,320 24,070 19,450 9,443 9,540 12.690 16,210 33,690 72,130 32,770 I Qc lcuhic teet per second! ______70,680 34,150 45,41111 33,720 26,940 19,130 9,580 7.461 9,97:l 17,740 48,780 56,340 31,6SO 8 1 -8.::l -13 6 -.5 1.2 11.9 -l.fi 1.5 -21.8 -21.4 9.4 44.8 -::n.9 -3.3 9 Qc { ~~: to JL~-~;,~;;(p~;~~,;t~f-Q~~-=== -9.2 -7.7 .1 5.6 1.0 -1.3 -7.0 -2.3 -.5 5.1 13.1 -10 4 -2 9 ::r:: 10 error due to reservmr-storage error ----- 9 -6.0 -.6 -4.4 10.9 -.3 8.4 -19.5 -20 9 4.4 31.1'1 -11.5 -.4 1--' 1 IL 0 !cubic feet per second I ______78,040 56,320 79,060 37,100 29.160 15,760 6,469 4,0.52 4.374 4,864 10,070 38,420 30,240 *"" 2 ILc !cubic feet per second!_ 73,750 56,610 76,700 39,150 28,840 14.480 5,2t1.5 3.492 4,164 5,119 10,590 35,220 29,360 3 ILc error I percent of IL0 1 -55 .5 -3 0 55 -1.1 -8.1 -18.3 -13.8 -4.8 5.2 5.2 -S.3 -2.9 4 .:lS11 converted to monthly flow_ 8,911 5.348 5,393 4,107 3,944 5 -980 -4.527 -7,996 -6,086 -6,030 68.5 219 5 .:l8c rate !cubic feet per second! 12,180 6,42R 6,289 1,920 -18 -2,206 -3,796 -3,388 -7,951 -8,882 0 0 1972 405 6 1 69,130 50,970 73,670 32.990 25,220 1.5,760 7,449 8.579 12,370 10,950 16,100 37,740 130,020 7 ~~ 1 ~~~:~ f::i ~=~ ~=~~~t =====--~=-===== 73,340 44.430 70,270 ~2.860 26,920 14,500 7,491 7,28R 7,552 13,060 19,470 35,220 29,360 8 6.1 -12 8 -4.6 -.4 6.7 -8 0 6 -15 0 -38 9 19 3 20 9 -6 7 -2 2 9 Qc {~~:\o i£:"-~~;~;(p~~~~,;t-oYQ~,-~-=- -6.2 .6 -3.2 6.2 -1.3 -8.1 -15.9 -6 ..5 -1.7 2.3 3.2 -8 ..5 -2.9 10 error due to reservoir-storage error -- 12.3 -13 4 -1.4 -6.6 8.0 .1 16.5 -!-i.5 -37.3 17.0 17.7 18 .7
IL 0 1cub1c feet per second I ______37,950 16.420 22,870 20,190 11,500 6,875 3,522 2,489 4,966 (21 ILc 1cub1c feet per second!_ 34,420 18,300 24,660 24.540 13,160 6,767 3,111 2.093 4,722 6,653 63,080 74,960 23,060 3 ILc error I percent of IL0 1 -9.3 11.-i 7.8 21.5 14.4 -1.6 -11.7 -15.9 -4.9 (21 4 .:lS11 converted to monthly flow ______296 3,572 6,65R 7,109 3,797 336 -2,536 -4,091 -3,081 (2) 5 1973 .:lSc rate !cubic feet per second! 0 ::l,282 5,489 6,003 2.725 -188 -2,889 -3,907 -1,278 -1,571 -7,441 2,157 183 6 Q 0 !cubic teet per second! ______37,6.50 12,8.50 16,210 13,080 7,701 6,539 6,058 6,580 8,047 13,970 70,440 85,930 "23,600 7 Qc !cubic feet per second I 34,420 1.'5,020 19,170 18,540 10,440 6,955 6,000 6,000 6,000 8,224 70,520 72,800 -122,880 R Q rota! ------S.6 1li.9 18.3 41.7 35.6 6.4 1.0 -8.8 -2.5 4 -411 .1 -15.3 -3.1 (2) 9 ei~;·or due to ILc error Ipercent of Q 0 1 -9 4 14 6 110 333 21 6 -1 7 -6.8 -6.0 -3.0 10 tlue to reservOir-storage error _ .8 2.3 7 2 8.5 13.9 8.0 58 -2 8 -22.4 1"1
'Adjusted to a 28-day February since HEG-3 1gnores leap year. 2 Final reservOir-storage data unavailable at hme of analysis. 3 0ctober through December values are prelimmary and subject to revision. "October through December results are based on preliminary observed streamflows at all ga~mg statwns suits, are within ±15 percent of the lL0 values due to differences in actual reservoir operation as which are based on observed data (table 7 and compared to the reservoir operatior in the fig. 8). This is especially gratifying considering reservoir-system model. The summation of both the vast opportunity for discrepancies in the ( 1) the storage changes and the total storage for 11 correlations for natural inflows, (2) diversion reservoirs in the Willamette River barin reser data, and (3) evaporation data. The errors in the voir system (Big Cliff and Dexter are orritted) for annual average flow for 1970-73 are all less than the rule curves defined for the model are tabu 3 percent. lated in table 9. Figure 9 illustrates the operation Additional insight to the modeling error can be differences between the model and the actual res gained by subtracting equation 2a from 2b and ervoir system. rearranging to obtain Operational differences are a commor problem in reservoir-release modeling. Rule curves are formulated during the reservoir's design phase in such a way that benefits from the reservoir will
Furthermore, multiplying through by 100/Q0 re be maximized over a long period. Es"entially, sults in they reflect the operation of the reservoir for ((av erage'' hydrologic conditions. Departures of the Q -Q 0 ) hydrologic conditions from ('average'' frequently ( CQO X 100 necessitate deviations from the design rule curve. A good example of such a case is the limited snow fall in the winter of 1972--73. Even by holding spring flows relatively low, it was only p'1ssible to fill the reservoir system to about 92 percent of The three bracketed terms in equation 5, fron1left desired capacity. Therefore, to meet derired flow to right, represent (fig. 8) (1) total Qc error, (2) Qc objectives in July through September, system error due to !Lc error, and (3) Qc error due to storage was depleted to less than 85 :r: 8rcent of reservoir-storage error. Table 6 (lines 8-10) desired capacity in August. The HEG-3 model (in summarizes these errors (with some roundoff er its present form) was not capable of such anticipa ror). Generally, errors due to reservoir-storage tion and only filled the system to about 76 percent error are more significant than those due to ILc and depleted it to less than 65 percent of desired error (tables 7 and 8 and fig. 8), especially when capacity. the total Qc error is large. Design rule curves (or parts the reo[) may also Most of the error related to reservoir storage is become outdated if new objectives are considered.
TABLE 7.-Model errors classified by absolute error limits
Percentage of months during the period January 1970 through September 1973 for wh1ch model errors are within absolute error lim1ts of- Type of model error' 5 10 15 20 25 30 35 .±0 45 percent percent percent percent percent percent percent percent percent EJL ______31.1 6.±.4 91.1 97 8 100.0 EQT _____ 26.7 .±8 9 60.0 71.1 84A 86.7 911 95.6 100.0 EQJL ______37.8 75.6 91.1 933 97.8 97.8 100.0 EQR _____ 35.6 64.4 75.6 84.4 93.3 9.56 97.8 100.0 'These symbols are used lin thts table and in table 8 and figure 81 to mdtcate absolute magmtude of the model errors as follows: EJL -[Lc error 1lme 3, table 61 EQr-total Qc error llme 8, table 61 EQJL -Qc error due to ILc error 1lme 9, table 61 EQR -Qc error due to reservOir-storage error I line 10. table 61
TABLE B.-Summary of modeling errors U.'ith absolute value exceeding 15 percent
Month Jan. Feb Mar Apr May June July Aug. Sept. Oct. Nov Dec. .. .. 4 4 4 4 .. 4 .. Number Q •) of 0 2 1 0 u 1 4 observatwns ------2 2 1
Average absolute EQT -- 23 ..8 17.7 31.7 35.6 21.8 27.3 19.3 32 .. 1 19.7 error EQJL -- 8 ..5 110 36.9 21.6 2 .. :3 1.7 2.3 7.4 10.1 { 19 ..5 2HI I percent I EQR --- 15.3 6.7 .±.8 13.9 2.5.5 17.0 9.6
H15 100
0 w 0 0 w w 0 w w u 80 w X u w X 0::: w 0 0::: 0 0 w 0 .....:1 w ..:r: GO .....:1 60 ;:::; ..:r: 0 ;:::; w G' ;a w ~ ...:l E-< w G' w 40 w 40 ~ w E-< ~ ~ E-< 0 ~ 0 zE-< w :20 zE-< 20 u w 0::: u w 0::: 0.. w 0..
0 0 15 25
ElL' IN PERCENT EQT' IN PER CENT
100
0 w 0 0 w w 0 w w u 80 w 80 X u w :X:w 0::: 0::: 0 0 0 w 0 .....:1 w .....:1 ..:r: 60 ..:r: 60 ;.:.., ;:::; G' w G'w ;a ;a ~ 0::: G' G' w 40 w 40 w w g ~ E-< ~ ~ ~ 0 0 E-< E-< z 20 z 20 w w u u 0::: w 0:::w 0.. Pot
0 25 30 35 15 20 40
EQIL' IN PERCENT EQR' IN PERCENT
FIGURE B.-Distribution of model errors, January 1970 through September 1973. A, ILc error. B, Total Qc error. C, Qc error due to ILc error. D, Qc error due to reservoir-storage error.
H16 TABLE 9.-Summation of total end-of-month storage and monthly storage changes specified by the design rule curces for 11 reservoirs in the Willamette Riuer basin reseruoir system
Svstem January February March April May June st~rage'
End-of-month total ___ ------715.74 1.417.30 1,812.50 2,186.70 2,306.82 2,306.82 Change dunng month ------0 701.56 395.20 :374.20 120.12 0
System October November December storage1 July August September
End-of-month total 2.224.00 2.067 .. 00 1.809.00 1,24-!.20 715.74 715.74 Change during month -82.82 -157.00 -258.00 -564 .. 80 -.528.46 0
'Storage quantities, shown m thousands of acre-feet, represent summatwn of indi\·idual destgn rule curves for the enttre system, wtth the exceptton of Big Cliff and Dexter reregulatton reservoirs.
--Design Rule Curves rnw c:: o Observed Data E- I!!. HEC-3 :.Iodel Results w ~ ~ u w
~ (:::) ~ ~ w 0 FIGURE 9.-Comparison of design, observed, and computed reservoir-system storage.
This has occurred in the Willamette River basin basin (especially if a portion of the total genera where increased flows in late August and in Sep tion capacity is inoperable), and (3) terr.porary tember are now used to stimulate fall fish runs. storage depletion and (or) discontinuation of re
Table 6 readily reveals this effect with Q0 consist leases for maintenance reasons. ently higher than Qc in August and September. Another important factor to consider in the dis Revision of the rule curve definitions in the model cussion of the HEC-3 model errors is the combi would have eliminated this particular bias, but nation of temporary flood storage and the detailed information was not available to make monthly time incren1ent. Several instances can the revision for this study. be found where the end-of-month deviatior above Other general possibilities for deviation from the rule curve (fig. 9) is due to a flood occurring the design rule curve at individual reservoirs are late in the month. An examination of ol:'served (1) floods which require temporary use of the flood daily data reveals that the system storage was control pool, (2) special operational procedures to depleted to the design rule curve shortly into the optimize short-term power production in the next month. Evacuation of the flood wat£-v-s any
H17 sooner would have created unnecessary flooding at Salem had the existing (1973) reservoir sys below the reservoirs. tem, subjected to present (1970) flow diversions, In summary, the verification results were con been in operation since 1926. Estimates of annual sidered acceptable. The HEC-3 model duplicated minimum low-flow rates based on these relations the actual system fairly well when considering should be significantly more reliable than those that ( 1) some of the errors are due to the monthly based on available data / Regulated
1. 01 1. 05 1.11 1. ~5 5 10 30 100 HECURRENCE INTERVAL, IN YEARS
FIGURE 10.-Frequency-discharge relations at Salem, 1926--73, computed from a simulated streamflow for existing !regu lated) conditions and from estimated streamflow for naturallunregulated) conditions.
H18 ment alternatives. Such alternatives or condi example, the temperature, sunlight, and flow tions might include ( 1) different demands on the conditions that combine for critical algal growth system (such as 1980, 2000, or 2020 flow diver conditions may not coincide with the annual sions), (2) different system-operation schemes minimum 7 -day or annual minimum n1onthly (such as deemphasis and (or) placing more em low-flow period. Frequency-discharge relation by phasis on one or more of the various authorized calendar months might be more applicable. Fig uses), (3l addition of reservoirs to the system, (4) ure 12 illustrates such relations for the individual the occurrence of more severe hydrologic condi months of July, August, and September b!lsed on tions (such as more extren1e droughts than have the simulated streamflows reflecting the 1970 di been experienced), and (5) combinations of the versions. Another potentially useful tool for above, ad infinitum. river-quality assessn1ent might be the annual The scope of this report does not permit minun1um flow for multimonth periods. Figure 13 analysis of all reasonable alternatives. However, shows frequency-discharge relations for the an to illustrate this type of model application, three nual minimum flow for consecutive 2- and 3- additional simulations were performed. Each of month periods based on the simulated stream these three simulations were identical to the pre flows reflecting the 1970 diversions. vious 48-year simulation, except that the flow di Only the Willamette River streamflow at versions used were those estimated for the years Salem is utilized in the above examplee., How 1980, 2000, and 2020. Thus, including the previ ever, model results may be obtained at any con ous simulation, 1926--73 data sequences of trol point (fig. 1 ). Therefore, similar evaluations monthly streamflows reflecting four levels of es could be made for the streamflow at several points timated flow diversions (table 4) are available for for basinwide river-quality assessment. comparison. Frequency-discharge relations of annual minimum monthly flows for all four simu SUMMARY AND DISCUSSION lations are presented in figure 11. These relations A reservoir-system model provides a useful tool may be used to determine the annual minimum for improving an available streamflow data base monthly low flow for any recurrence interval which consists of streamflow data that have been (hereafter denoted by tQ m , where t is the recur observed during a period of changing conditions. rence interval and Qm denotes average monthly Applicability of the U.S. Army Corps of En flow rate). gineers' HEC-3 reservoir-system model to the Also, as mentioned above, estimates of annual W illamette River basin reservoir system is ver minimum 7-day low flows for any recurrence ified by comparing model results with ol~~erved interval (tQ 7, where t indicates recurrence inter stream-flow at Salem for a 4-year period (1970-- val and Q7 denotes average 7 -day flow rate) may 73. In general, modeling errors for this verifica be obtained using the t Q m data. The relation of tion period are within reasonable limits. Predic annual minimum 7 -day to annual minimum tive errors could possibly be reduced by (1) revis monthly low flows (fig. 5) may be expressed as ing model input data to better define actual reservoir-system operation; (2) refining unregu (6) lated streamflow estimates by using water budget computations along with corr~lation Table 10 summarizes estimates of annual mini analyses; and (3) using more refined evaporation mum monthly and annual minimum 7 -day flows estimates and including precipitation data in the for the 1970 and 2020 levels of flow diversions. analysis. This last source of possible error applies Also shown is the percent reduction in these flows to the entire basin. The first two, however, could resulting from the increased flow diversions proj possibly be isolated to one or more segm~nts of ected for 2020 relative to the estimated flow di the basin by comparing model results with ob versions of 1970. A DO model could be used to served streamflow at other control points in the assess the impact that the increased flow diver basin. Also, a longer verification period could add sions (reduced minimum flows) would have on DO increased confidence in model applicabilit:r. concentrations. Despite the above limitations, the HEC-3 Other low-flow periods may also be useful for reservoir-system model is used for four ::-imula assessing potential river-quality problems. For tions of monthly streamflow data to demonstrate
H19 1- r-----..... - ~ 1- ~ 0" ~ ~ 1- v - 1- ··~ I- ~ ~---~ t-- 0 -
f-
(C)
1- r-- v - 1- v VVv 1- ~ ·"'vo 1- ~ 1- - 516/ 1- ~ - 396t ~ 1- f'- 318~
1- - 50
(D)
1. 01 1. 05 1.11 1. 25 2 5 10 25 50 100
RECURRENCE INTERVAL, IN YEARS
FIGURE H.-Frequency-discharge relations at Salem, 1926---73, computed from simulated streamflows reflecting the existing reservoir system subjected to different estimated flow diversions. A, 1970 flow diversions. B, 1980 flow diversions. C, 2000 flow diversions. D, 2020 flow diversions.
TABLE 10.-Determination of tQm and tQ7 at Salem for the TABLE 10.-Determination of tQm and tQ7 at Salem for the simulated streamflou•s reflecting the 1970 and 2020 flow simulated streamflows reflecting the 1970 and 2020 flou.• diversions dit~ersions-Continued
Reductwn Reduction 1 1 tQ7" Simulatton tQm tQ7" in flow S1mulatwn 1Qm m flow using- lyearsl 1tP/s1 1lt"/sl I percent 13 using- I years I ltt"/sl lft"/si I percent is
10 6,1.'\0 5.380 10 5,160 4,490 17 1970 2020 25 3,960 3,450 33 diYersions 25 5,880 .5,120 diYersions 50 5,700 4.960 50 3,180 2,770 44
1From figures 11 tor 1970 and 2020 flow dlVersions. "Percent reduction oflow flows at Salem reflecting 2020 diverswns as compared 2 Computed by equatiOn 6, tQ7=0.87tQ 111 • to those reflectmg 1970 di verswns.
H20 15.---r------.-----~-----r------~------~------~------r---~--~400 350 10 300 250 0 200 z 0 u 150 (A) rt:J"" 0:: 4----~------~----~----~------~------~------~------~--~--~ 0..""
- - - f- ~ f- --a---e- .... - r- ~ r- .~ .... ,..,.., f- 0 u r-- f- - (C)
1.01 1. 05 1.11 1. 25 2 5 10 25 50 100
RECURRENCE INTERVAL, IN YEARS
FIGURE 12.-Frequency-discharge relations at Salem, 1926--73, computed from discharges for calendar months. A, July. B, August. C, September.
1. 01 1. 05 1.11 1. 25 2 5 10 25 50 100
RECURRENCE INTERVAL, IN YEARS FIGURE 13.-Frequency-discharge relations at Salem, 1926-73, computed from mm1mum multimonthly discharge. A, 2-month minimum discharge. B, 3-month minimum discharge. potential applications. Each simulation utilizes tion of the existing reservoir system. Different di identical input data for (1) defining system inputs version data, reflecting estimated flow diversions and losses with unregulated monthly streamflow for the years 1970, 1980, 2000, and 2020, are used and evaporation data for a 48-year period (192~ for each simulation. 73) and (2) defining the operation and configura- Frequency-discharge relations of low flow at
H21 Salem based on these simulated streamflows for sion any other tool that could provide such flexi regulated conditions and on the estimated bility for analyzing planning or managemental streamflow for natural conditions are used to ternatives in the Willamette River basin. demonstrate potential applications of simulated streamflow data. Detailed examples illustrate (1) REFERENCES CITED use of low-flow characteristics reflecting existing Draper, N. R., and Smith, H., 1966, Ap":llied regression conditions and those reflecting natural conditions analysis: New York, John Wiley and So:'l.s, Inc., 407 p. as a basis for assessing the total impact that the Gleeson, G. W., 1972, The return of a river, the Willamette existing reservoir system has had on DO concen River, Oregon: Advisory Comm. Environmental Sci. and trations at Salem and (2) use of low-flow charac Technology and Water Resources Inst., Oregon State Univ., Corvallis, 103 p. teristics reflecting existing conditions and those Hardison, C. H., 1969, Accuracy of streamflovr characteristics, reflecting estimated 2020 flow diversions as a in Geological Survey research 1969: U.S. Geol. Survey basis for assessing the impact that the higher flow Prof. Paper 650-D, p. D210-D214. diversions projected for the future will have on Hines, W. G., Rickert, D. A., McKenzie, S. W., and Bennett, J. DO concentrations at Salem. Other potential ap P., 1975, Formulation and use of practical models for river-quality assessment: U.S. Geol. Survey Circ. 715-B, plications of the reservoir-system model are p. 13. briefly discussed. Jennings, M. E., Shearman, J. 0., and Bauer, D. P., 1976, Each reader, of course, is free to pass independ Selection of streamflow and reservoir-rdease models for ent judgment as to the applicability of the simu river-quality assessment: U.S. Geol. Survey Circ. 715-E, 12 p. lated streamflow data. The author feels that the Rickert, D. A., and Hines, W. G., 1975, A pra-:tical framework discharge-frequency relation based on the for river-quality assessment: U.S. Geol. Survey Circ. streamflow data simulated using estimated 1970 715-A, 17 p. flow diversions (fig. 11A) is a more reliable esti Texas Water Development Board, 1972, Economic optimiza mate of long-term basin response to existing con tion and simulation techniques for management of re ditions that can be obtained by using the limited gional water resource systems, river h'lsin simulation model, SIMYLD-II program descriptio'l: Texas Water observed data that are applicable (fig. 3). Also, Devel. Board, 106 p. comparison of figures 11A-D provides a sound es U.S. Army Corps of Engineers, 1968, HEC-3, reservoir sys timate as to the relative decrease in low flows as a tems analysis: Hydrol. Eng. Center U ~ers Manual No. result of increased future flow diversions. 23-53, 86 p. Assuming that either (1) the model is adequate U.S. Geological Survey, 1973, Water res0urces data for Oregon-part 1, surface water records: 409 p. as described herein or (2) it can easily be altered Willamette Basin Task Force, 1969, Appendix M, Willamette to yield more acceptable results, the potential basin comprehensive study: Pacific Northwest River Ba benefits of using it are obvious. It is hard to en vi- sins Comm. Rept., p. II-1-II-34.
H22